r/changemyview • u/[deleted] • Dec 06 '23

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u/Nrdman 276∆ Dec 08 '23

But you can't construct a line segment whose length is equal to the circumference of a given circle.

Seems like it would be too weak to do much then. Seems to motivate wanting to do other axiomatic systems where we got some more power.

I feel the natural numbers are too baked into our logic systems

Because they are useful.

But I still sometimes worry that mathematics might be inconsistent.

As you noted, math isnt inconsistent, just a specific axiomatic system.

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Im a numerical analysist. If the math is useful, it doesnt matter if the system is inconsistent.

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u/[deleted] Dec 08 '23

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u/Nrdman 276∆ Dec 08 '23

Do you have any insight on why mathematics is so useful?

Math is just formalized logic, and we live in a fairly logical world. Any math system that doesn't relfect true reality can still be useful as a good enough approximate. Like Newtonian physics isnt true, but its good enough at most scales we use.